The time evolution of the components in the patterns/systems is in general fluctuation driven stochastic process which can be well described in a probabilistic manner [1]}. The inherent fluctuations in the dynamics of the constituting variables arise from the internal (due to inter-molecular interaction) and external (due to fluctuations driven by surrounding the system i.e. temperature fluctuation, environmental fluctuations etc) fluctuations and have variety of roles in regulating the system [2]}, [3]}. The trajectory of the variables of the pattern/system and their realizations can be obtained using the Master equation, which is the discrete form of the Chapman-Kolmogorov equation [1]}, [5]}, constructed from the information of the transitions of the states due to inter-variables interaction [2]}, [7]}, [8]}. On the other hand, computationally, the trajectory of each variables in the system can be traced using Monte carlo like stochastic simulation algorithm (SSA) due to Gillespie [9]}. The stochastic approach has wide variety of applications, ranging from microscopic biomolecules [10]} to macroscopic ecology [11]} to cosmology [12]}, and then to finance [13]}, [14]}, cryptography [15]} etc.
